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In this talk, I will briefly introduce my work on optimal list decoding and list recovery of algebraic codes, their connections to expanders and pseudorandomness, and some future directions I am interested in exploring.
A welcome event for all new Simons fellows to introduce them to the Simons Institute community. All new fellows will present a 10-minute talk followed by 5 minutes for Q&A with the aim of making introductions to each other, program participants, and the...
Random matrix theory (RMT) is the area of probability theory concerned with spectral behavior of large matrices with random entries. Historically, RMT originates from statistics through the work of Wishart in 1920s and, independently, from mathematical physics thanks to Wigner in 1950s. Wigner first had the brilliant idea to model complicated operators arising in the study of many-body quantum systems as random matrices. It has since been rigorously established that spectra of certain classical random matrix ensembles do, in fact, exhibit the behavior that is expected from deterministic quantum chaotic operators (the latter is mostly out of reach of formal mathematical treatment at this time). I will briefly mention some classical results in RMT, in particular as they relate to quantum chaos. I will also discuss an alternative, yet related, approach to modeling quantum chaos using graph theory and share related open problems.
The 5th annual Quantum Industry Day will bring together scientists from academia and industry for an interactive exchange on directions and opportunities in quantum computing. This is an invitation-only event and registration will be required for all...
I will survey the remarkable progress on explicit constructions of randomness extractors for structured sources, including independent sources, small-space sources, and related models. Much of this progress has been driven by the development of powerful new primitives, such as non-malleable extractors, correlation breakers, and leakage-resilient extractors. I will discuss these notions, the connections between them, and discuss interesting open directions.
In this series of talks, we introduce coboundary expansion, a generalization of graph expansion to higher-dimensional complexes. Coboundary expansion can be understood both as a high-dimensional isoperimetric inequality and as a local testability property of codes arising from these complexes. We will first present the coding-theoretic definition of coboundary expansion. We will then introduce Gromov’s cone method, a fundamental technique for proving coboundary expansion. Finally, we will dive into an application of coboundary expansion: the Evra–Kaufman result that local spectral expanders with coboundary-expanding links give rise to locally testable codes.
Minicourse on quantum ergodicity, mostly on graphs, with some extensions and questions on manifolds.